Stochastic quantization method for spinning particles in a gravitational plane wave field

The exact and analytic Green functions for spinning relativistic particles in interaction with a gravitational plane wave field are obtained within the Stochastic Quantization Method of Parisi and Wu. We have separated the classical calculations from those related to the quantum fluctuations. The problem has been solved by using a perturbative treatment via the Langevin equation relying on phase and configuration spaces formulation.      

Motion of an ideal fluid in the field of a plane gravitational wave

An exact solution of the equations of relativistic hydrodynamics is found which describes the motion of an initially uniform ideal fluid in the field of a plane gravitational wave of arbitrary amplitude and polarization. For all solutions we find that the pressure and energy density develop singularities on the singular surface, and the velocity of the fluid in the direction of propagation of the gravitational wave approaches the speed of light. In the case of the equation of state =p, the solution becomes intrinsically unstable and describes the generation of sound waves.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 96–99, November, 1982.     

On the motion of test particles in the field of a plane gravitational wave

The motion of test particles in the field of a plane gravitational wave is studied in order to derive some general properties of such motion, especially the possibilities of repeated meetings of two inertially moving particles.The work was done at Moscow State University, Moscow.     

Ideal fluid with short-range scalar interactions in the field of a plane gravitational wave

An exact solution of the self-consistent equations of relativistic hydrodynamics and the scalar field equation is obtained. The solution describes motion of a fluid with short-range scalar interactions in the field of a plane gravitational wave.     

How to lasso a plane gravitational wave

Beginning with the stress-energy tensor of an elastic string this paper derives a relativistic string and its form in a parallel transported Fermi frame including its reduction to a Cosserat string in the Newtonian limit. In a Fermi frame gravitational curvature is seen to induce three dominant relative acceleration terms dependent on: position, velocity and position, strain and position, respectively. An example of a string arranged in an axially flowing ring (a lasso) is shown to have a set of natural frequencies that can be parametrically excited by a monochromatic plane gravitational wave. The lasso also exhibits, in common with spinning particles, oscillations about geodesic motion in proportion to spin magnitude and wave amplitude when the spin axis lies in the gravitational wave front.     

Relativistic gas in a gravitational field

Equations describing the kinetics and hydrodynamics of a relativistic gas in a gravitational field are obtained using the concept of a gravitational field as a physical field in a pseudo-Euclidean space-time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 17–20, September, 1982.     

Weak processes in the field of a gravitational wave

The influence of a gravitational wave on the cross section of a decay process is analyzed in this paper. The cross section for a decay in the presence of a strong gravitational wave is found.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 25–30, December, 1984.     

Fabry-Perot cavity in the field of a gravitational wave

The structure of the electromagnetic field inside a laser cavity—a gravitational-wave detector—is studied. The properties of the spatial and temporal phases of the standing electromagnetic wave are discussed in detail and the corrections appearing in the electric field of the wave as a result of the action of gravitational radiation on the optical system are determined. Zh. éksp. Teor. Fiz. 113, 398–408 (February 1998)     

Worldline path integrals for a Dirac particle in a weak gravitational plane wave

The problem of a relativistic spinning particle interacting with a weak gravitational plane wave in (3+1) dimensions is formulated in the frame work of covariant supersymmetric path integrals. The relative Green function is expressed through a functional integral over bosonic trajectories that describe the external motion and fermionic variables that describe the spin degrees of freedom. The (3+1) dimensional problem is reduced to the (1+1) dimensional one by using an identity. Next, the relative propagator is exactly calculated and the wave functions are extracted. PACS 04.30.-w; 03.65.Ca; 03.65.Db; 03.65.Pm     

On the gravitational field of a plane plate in general relativity

It is shown that a static solution of the Einstein equations inside an infinite plate of an ideal liquid with continuous metric coefficients and their first derivatives cannot have a plane of mirror symmetry. As a consequence, the boundaries of the plate are joined with qualitatively different vacuum solutions on both sides of the plate.     

The electric field induced by a gravitational wave in a superconductor: a principle for a new gravitational wave antenna

In this paper we investigate the effect of gravitational waves (GW) on a superconductor. We find that the key properties of a superconductor, namely zero resistance and perfect diamagnetism, give rise to an important new effect, the presence of an induced electric fieldE(r, t) in the interior of the superconductor. TheE field reacts with the ions and superelectrons. We argue, that not only is the finding of the coupled interactions of gravitation, electromagnetism and superconductivity inherently interesting, but that the inducedE field might provide a significantly more sensitive means of detecting gravitational waves. It appears likely that existing resonant-mass superconducting antennas withL - 3m,Q - 10⁸ could be readily modified to detectE fields induced by GWs of dimensionless amplitudeh - 10^–24 This essay received the first award from the Gravity Research Foundation for the year 1989—Ed.     

Bose gas in gravitational field

The Bose gas in an arbitrary curved space-time is considered. A method of construction of the thermodynamic potential of a quantum gas by means of a finite-temperature Green's function is proposed. On this basis the Bose and Boltzmann distributions are derived. The behavior of the chemical potential is investigated. The phenomenon of Bose-Einstein condensation is discussed.     

Resonant generation of plasma oscillations by a plane gravitational wave

An exact solution of the universal Maxwell equations linearized in the amplitude of the induced field is found with the help of a previously found exact solution of the kinetic equation with a model collision integral. Two oscillation modes arise under the action of a gravitational wave in a plasmalike medium: an undamped wave with the frequency of the gravitional wave and a damped one with the plasma frequency. When these frequencies coincide, a resonance arises, as a result of which the amplitude of the electric oscillations increases sharply.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 74–77, January, 1985.     

A new exact solution for colliding gravitational plane waves

A new exact solution of the vacuum Einstein equations describing the spacetime following the collision of two plane impulsive gravitational waves, each supporting a plane gravitational wave, is obtained. The solution has been extended prior to the instant of collision and the main features of the resulting space-time have been analyzed, using the Newman-Penrose formalism. It is shown that the result of the collision is the development of a singularity of the spacetime due to the simultaneous focussing of the two plane waves.     

Nonlinear theory of the compressible gas flows over a nonuniform boundary in the gravitational field in the shallow-water approximation

A set of equations is derived for the motion of a compressible ideal gas over a nonuniform boundary in the gravitational field in the shallow-water approximation. Classical simple waves are shown not to be the solutions to this set of equations. Generalized simple waves are found to exist only in the case of a linear underlying-surface profile. All continuous and discontinuous solutions are obtained in an explicit form for the case of the boundary in the form of an inclined plane, and an analytical solution is found for the problem of the decay of an arbitrary discontinuity. This solution consists of four wave configurations. Necessary and sufficient conditions are determined for the existence of each configuration.